The 12 points on the clock
Source: China South East Mathematical Olympiad2011
August 18, 2011
combinatorics proposedcombinatorics
Problem Statement
12 points are located on a clock with the sme distance , numbers are marked on each point in clockwise order . Use 4 kinds of colors (red,yellow,blue,green) to colour the the points , each kind of color has 3 points . N ow , use these 12 points as the vertex of convex quadrilateral to construct convex quadrilaterals . They satisfies the following conditions:
(1). the colours of vertex of every convex quadrilateral are different from each other .
(2). for every 3 quadrilaterals among them , there exists a colour such that : the numbers on the 3 points painted into this colour are different from each other .
Find the maximum .